Assume that the heights of men are normally distributed with a mean of "71.3" inches and a standard deviation of 2.1 inches. If 36 men are randomly selected, find the probability that they have a mean height greater than 72.3 inches. Round to four decimal places.
Answer:
0.0021 = 0.21% probability that they have a mean height greater than 72.3 inches.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Assume that the heights of men are normally distributed with a mean of "71.3" inches and a standard deviation of 2.1 inches.
This means that [tex]\mu = 71.3, \sigma = 2.1[/tex]
Sample of 36:
This means that [tex]n = 36, s = \frac{2.1}{\sqrt{36}} = 0.35[/tex]
Find the probability that they have a mean height greater than 72.3 inches.
This is 1 subtracted by the pvalue of Z when X = 72.3. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{72.3 - 71.3}{0.35}[/tex]
[tex]Z = 2.86[/tex]
[tex]Z = 2.86[/tex] has a pvalue of 0.9979
1 - 0.9979 = 0.0021
0.0021 = 0.21% probability that they have a mean height greater than 72.3 inches.
What is the mean for the data shown in the dot plot? 4 5 6 10
Answer:
Mean = 6.25
Step-by-step explanation:
Data values: 4, 5, 6, 10
Mean = (Sum of all values)/(Number of values)
Mean = (4 + 5 + 6 + 10)/4
Mean = 25/4
Mean = 6.25
The mean for the data shown in the dot plot is 6.25.
The given data is 4, 5, 6 and 10.
We need to find the mean for the data shown in the dot plot.
What is the dot plot?A dot plot is used to encode data in a dot or small circle. The dot plot is shown on a number line that displays the distribution of numerical variables where a value is defined by each dot.
Now, mean = Sum of all the observations / Total number of observations
=(4+5+6+10)/4
=25/4
=6.25
Therefore, the mean for the data shown in the dot plot is 6.25.
To learn more about the dot plot visit:
https://brainly.com/question/22746300.
#SPJ2
What fraction of the whole are the blue piece, the orange piece, the red piece, and the purple piece. How do you know?
Answer:
blue piece is 1/2 because it takes up half of the square, the purple is only 1/4 because it would take 4 purple to fill the big square and the orange is half of the purple so it takes double of pieces so 8 pieces which is 1/8
Edgar and his 4 friends want to share the cost of a meal equally. They order
3 large pizzas and 5 small drinks. If they leave a tip of $8.10, how much does
each person pay?
Answer:
Each person pays $9.72
Step-by-step explanation:
Add up the cost of the large pizzas, small drinks, and the tip, then divide by 5.
f(16) – f(0) when f (x) = 4x – 8?
Answer please and explain
Answer:
18.84956, 18.84 if rounded to the nearest hundredth, and 18 if rounded to nearest whole number.
Answer:
Step-by-step explanation:
PLEASE HELP !! ILL GIVE BRAINLIEST !!
Answer:
<ONP and <MNP
Step-by-step explanation:
GUYS HELP PLEASE ASAP You are deciding between two jobs. Offer 1 is $40,000 and a raise of
$4,000 per year. Offer 2 is $52,000 and a raise of $2,000 per year. In how
many years will both jobs pay you the same salary? What would the salary
be? Which offer should you choose if you plan on working for 10 years?
Answer:
offer 1= you get 80k for the first offer for 10 years.
offer 2= you get 72k for the second offer for 10 years.
Result:
offer one would be better as you would get more money.
The starting numbers for x and y are already entered in a table below the blanks in the table represent the next two terms for each of the patterns the pattern for the X-Files is added to pattern for the y values it at 4 which graph represents the order pairs of first three terms of the pattern from the table?
Answer:
it is this one
Step-by-step explanation:
because since x is 4 and y is 8 that one matches up better than any other one
Can someone please do my math work I am gonna lose my permit soon and my mom just passed and I'm struggling
What is the equation of a line with a y-intercept at (0, 2) and a slope of 3?
a. y = 2x + 3
C. y = 3x + 2
b. y = 3x - 2
d. y = -2x + 3
Answer:
answer is C
the slope is 3 and the intercept is (0,2) which is 2
What is the median of the data set?
73, 20, 63, 23, 20, 40, 67
Answer:
40
Step-by-step explanation:
if you line the numbers up like so you will see the number in the middle is 40
aka the median
20,20,23,40,63,67,73
The sequence below shows the
number of cells in a sample at
the end of the four hours. 6, 12,
24, 48, which recursive formula
models the sequence?
Answer:
Step-by-step explanation:
Option B 2. Now is the correct answer because when we multiply 6 by 2 we get 12 then we multiply 12 by 2 we get 24
n is an integer such that -2 <n<3
Write down all the possible values of n.
Answer:
................................
Which is the equivalent expression, please help!
Answer:
The first choice
Step-by-step explanation:
find x with the formulaaa
Which of the following is NOT an element of impressionistic painting.
A. Photography
B. Mood
C. color
D. Perspective
Please help me answer this
Answer:
A. Photography. I couldn't say this is in mathematics but okay :)
How many solutions does the following system of equations have?
y = 2x + 6
y = 4x + 12
A) One solution
B) Infinitely Many Solutions
C) No Solution
D) Two Solutions
Answer:
only one
Step-by-step explanation:
because by everymethod answer is -3
Answer:
D
Step-by-step explanation:
What is the radius of a Ø6.75" circle? 3.375" or 3.750" or 4.375" or 6.750"
Answer:4.375
Step-by-step explanation:
What is the value of 1 − ( 2 − ( 3 − ( 4 − 5 ) ) ) 1 − ( 2 − ( 3 − ( 4 − 5 ) ) )
Answer:
51
1−2+3−4+5−.....+101
=(1+3+5+.....+101)−(2+4+6+.....+100)
=(1+3+5+.....+101)−2(1+2+3+.....+50)
=(51)
2
−2(
2
50(50+1)
)
=2601−2×1275
=2601−2550
=51
In circle Z, BZ = FZ, BZ 1 CA, FZ 1 DC DF = 18 in.
What is BC?
Answer:
18 in.
Step-by-step explanation:
I just took the quiz
Answer:
The dimenssion of BC is - 18in.
Step-by-step explanation:
Definition of circle:
The set of all points in the plane that are a fixed distance (the radius) from a fixed point is called a circle . A radius is the distance between any two points on a circle and the center. Any two radii have the same length according to the definition of a circle.
Step 1:
in Δ[tex]ZFC[/tex] and Δ[tex]ZFD[/tex]
[tex]ZD = ZC[/tex] ( Radius of the circle will be same )
[tex]ZF= ZF[/tex] (Common side in both triangle)
[tex]$\angle Z F C=L I P D=90^{\circ}[\because F Z \perp D C][/tex]
So from Side Angle Side theorem,
[tex]$\triangle Z F C \cong \triangle Z f D$[/tex]
So, [tex]$F C=F D=18 in.[/tex]
Step 2:
[tex]$\triangle B C Z$[/tex] and [tex]$\triangle F C Z$[/tex]
[tex]$B Z=F Z \quad$[/tex] (Given)
[tex]CZ = CZ[/tex] (Common side in both the triangle)
[tex]$\angle Z B C=\angle Z F C=90^{\circ} \quad[\because \overline{B Z} 1 \overrightarrow{C A}$[/tex] and [tex]$$\overline{F 2} \perp \overline{D C}]$$[/tex]
So from sides side angle theorem,
Δ[tex]BCZ[/tex]≅ Δ[tex]FCZ[/tex]
So, [tex]BC = FC[/tex]
Hence [tex]BC = 18in.[/tex]
Learn more about Circle here,
https://brainly.com/question/24375372
#SPJ2
Please please i need help i will mark u brill
Answer:
Step-by-step explanation:
8d + 54 = 150
Putting value of D = 12 in the equation
8(12) + 54 = 150
96 + 54 = 150
150 = 150
Bringing like terms on one side
150 - 150 = 0
Answer:
Correct.
Step-by-step explanation:
8d+54=150
Putting d=12 we get
8(12)+54=150
96+54=150
150=150
14/7 = n/21 what is the value of n
Answer:
n=42
Step-by-step explanation:
14/7=n/21
2=n/21
42=n
n=42
Answer:
n = 42
Step-by-step explanation:
14/7 = 2
42/21 = 2
Find the answer
5/8 + (2/3 - 1/4) =
Answer:
25/24
Step-by-step explanation:
simplify: 2/3-1/4 to 5/12
5/8+5/12
=25/24
The ratio of boys to girls in Ms. Gonzalez's class is 3 to 4. There are 12 girls in the class. What is the total number of students in Ms. Gonzalez's class?
Answer:
there are 21 students in her class.
Step-by-step explanation:
Since the 12 girls corresponds to the 4 in the ratio, I multiplied the 3 by three to get the amount of boys. then add the boys to the girls to get 21 students.
10. Beth has a wooden box. The inside of the box is 5 inches wide, 8.25
inches long, and 4.5 inches tall.
Answer:
185.625in^2
Step-by-step explanation:
This is volume right?
5*8.25*4.5=
Room's volume is 600 m^3. There is 800 ppm (parts per million) of CO2 in the room.
Fresh air, with the CO2 concentration of 400 ppm starts flowing into the room at the rate of 40 m^3/min. The pressure in the room is constant, so an equal amount of stale air flows out as fresh air flows in, and the CO2 is evenly distributed.
a) Form the differential equation for the amount of CO2 in the room.
b) Solve this differential equation
c) What is the CO2 concentration of the room after fresh air has been flowing in for 30 minutes?
Answer: C
Step-by-step explanation: Hope this help :D
factor 6x^4+42x^2+12
Answer: 6(x^(4)+7x^(2)+2)
Step-by-step explanation: Factor 6 out of 6x^(4)+42x^(2) +12
brainliest or a thank you please :)) <33
How do I put 4/3 on a fraction number line
Answer:
you would put it as four thirds
Step-by-step explanation:
Answer:
Lets break this down.
4/3 can be simplified as 3/3 and 1/3.
3/3 can also be simplified into 1.
That leaves us with a mixed fraction as 1 1/3.
Now that we know our mixed fraction, we must locate this on a number line.
I drew 3 marks on a number line to demonstrate this, along with a indicator showing where 1 1/3 is.
Since 1 1/3 has one whole, we know that 1 1/3 is greater than 3/3.
We locate 1 on the number line, which is directly in the middle.
Now, we have to move one more to the right, since we have a remaining 1/3.
This leaves us where we are on the photo provided.
Hope this helps! c:
According to some sources, the African continent has about 170 million Internet users. According to the bar graph, which statement is true?
Africa has fewer users than the Middle East.
Africa has more users than Asia.
Africa has more users than Europe but fewer than Asia.
Africa has more users than the Middle East but fewer users than North America.
Answer:
The last answer choice
Step-by-step explanation:
Interpretation of internet users
Middle East - about 100 million
North America - about 250 million
Europe - about 500 million
Asia - over 1 billion
Now lets look back at the question.
If Africa has 170 million internet users, according to the graphs, which statement is true.
"Africa has fewer users than the middle east"
This is false as Africa has 170 million users whereas The middle east has about 100 million users
170 mil > 100 mil therefore the statement is false
"Africa has more users then Asia"
This is also false as Asia has the most internet users at 1 billion
Africa has no where near as many users at 170 million users therefore the statement is false
"Africa has more users than Europe but fewer than Asia."
We have already identified that Africa has fewer users than Europe so this one could be it if the other part is true.
"Africa has more users than Europe" This is false as Europe has 500 million internet users while Africa only has 170 million users
Therefore this statement is false
"Africa has more users than the Middle East but fewer users than North America."
Africa has more internet users than the Middle East ( 170 mil > 100 mil ) and fewer users than North America ( 250 mil > 170 mil )
therefore this is the correct statement
